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How to solve geometry word problems that involve geometric figures and angles described in words? You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

### Geometry Word Problems Involving Area

*x *= original width of rectangle

Sketch the figure

*lw*

*x*.

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

2x + 8 = 0 ⇒ 2x = -8 ⇒ x = -4

**Writing quadratic equations to solve word problems: Area of a triangle**

Example:

The height of a triangles is 3 cm more than its base. The area of the triangle is 17 cm^{2}. Find the base to nearest hundredth of a cm.
**Find the Dimensions of a Rectangle Word Problem**

Example:

The length of a rectangle is 5 units more than twice its width. If the area is 250 sq. units. then find the dimensions of the rectangle.

**Solve Area World Problems by Factoring**

Example:

A garden that is 4 meters wide and 6 meters long is to have a uniform border such that the area of the border is the same as the area of the garden. Find the width of the border?

**Example of geometry word problem that involves area**

Example:

A rectangle is twice as long as it is wide. If the area of the rectangle is 98 cm^{2}, find its dimensions.

More Lessons for Algebra

Math Worksheets

How to solve geometry word problems that involve geometric figures and angles described in words? You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Example:

A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

Solution:

Step 1: Assign variables:

LetSketch the figure

Step 2: Write out the formula for area of rectangle.

A =Step 3: Plug in the values from the question and from the sketch.

60 = (4*x* + 4)(*x* –1)

Use distributive property to remove brackets

60 = 4*x*^{2} – 4*x* + 4*x* – 4

Put in Quadratic Form

4*x*^{2} – 4 – 60 = 0

4*x*^{2} – 64 = 0

This quadratic can be rewritten as a difference of two squares

(2*x*)^{2} – (8)^{2} = 0

Factorize difference of two squares

(2*x*)^{2} – (8)^{2} = 0

(2*x* – 8)(2*x* + 8) = 0

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

2x + 8 = 0 ⇒ 2x = -8 ⇒ x = -4

Since *x *is a dimension, it would be positive. So, we take *x* = 4

The question requires the dimensions of the original rectangle.

The width of the original rectangle is 4.

The length is 4 times the width = 4 × 4 = 16

Answer: The dimensions of the original rectangle are 4 and 16.

Example:

The height of a triangles is 3 cm more than its base. The area of the triangle is 17 cm

Example:

The length of a rectangle is 5 units more than twice its width. If the area is 250 sq. units. then find the dimensions of the rectangle.

Example:

A garden that is 4 meters wide and 6 meters long is to have a uniform border such that the area of the border is the same as the area of the garden. Find the width of the border?

Example:

A rectangle is twice as long as it is wide. If the area of the rectangle is 98 cm

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